Monday, July 9, 2012

Nonlinear models - Results and Tests

After computing parameters for nonlinear models using least squares (LQ) method of estimation, next step was to add result statistics and writing tests comparing results from other statistical package to those from statsmodels.

Model and Results
The model used for analysis was the 'Misra1a' model selected from NIST nonlinear models. Dataset misra was addded to datasets directory. Parameter estimates and standard error of residuals were provided in the NIST data file. Other results of nonlinear regression analysis of the given model were obtained from Gretl. Reason for choosing gretl was that it uses the same Minpack module for LQ estimation that is used in scipy.optimize. All the results were stored in python class Misra1a.

Four sets of 18 tests ( 2 start values with and without the jacobian ) provided in were run and we obtained exact matches upto 4 decimal places.

Weighted NLS
Weights (1 for the first seven observations and 0.49 for the next seven observations) were provided while fitting the data.
Gretl does not provide the feature of weighted nls and hence we had to use results from R which has the provision to do so. Test class for weighted NLS was added to and 14 tests were added. Only one test regarding confidence intervals of parameters failed which is only a precision issue (No digits after the decimal match).

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